5a^2+8a=13a^2

Solution for 5a^2+8a=13a^2 equation:

5a^2+8a=13a^2

We move all terms to the left:

5a^2+8a-(13a^2)=0

determiningTheFunctionDomain
5a^2-13a^2+8a=0

We add all the numbers together, and all the variables

-8a^2+8a=0

a = -8; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-8)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-8}=\frac{-16}{-16}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-8}=\frac{0}{-16}
=0
$